Digit patterns and Coleman power series

Details Digit patterns and Coleman power series Digit patterns and Coleman power series

2005-10-17

arxiv.org/abs/math/0510355v1

Mathematics

Number Theory

LaTeX, 15 pages

Scientific paper

Our main result is elementary and concerns the relationship between the multiplicative groups of the coordinate and endomorphism rings of the formal additive group over a field of characteristic $p>0$. The proof involves the combinatorics of base $p$ representations of positive integers in a striking way. We apply the main result to construct a canonical quotient of the module of Coleman power series over the Iwasawa algebra when the base local field is of characteristic $p$. This gives information in a situation which apparently has never previously been investigated.

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